# Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product, and result of the division of fractions or mixed numbers. It will also convert fraction into decimal number and into improper fraction (if possible).

## Solution

**Your input: find the sum, difference, and product of two fractions, the result of the division; convert them into decimal.**

**The fractions are: $$$2\frac{3}{7}$$$, $$$\frac{5}{9}$$$**

Convert $$$2\frac{3}{7}$$$ into an improper fraction.

Rewrite $$$2$$$ as $$$\frac{14}{7}$$$

Add the fractions: $$$2\frac{3}{7}=\frac{14}{7}+\frac{3}{7}=\frac{17}{7}$$$ (we just add the numerators, since the denominators are equal).

So, $$$2\frac{3}{7}=\frac{17}{7}$$$

## Fractions addition

Multiply the numerator and the denominator of the first fraction by $$$9$$$: $$$\frac{17}{7}=\frac{153}{63}$$$

Multiply the numerator and the denominator of the second fraction by $$$7$$$: $$$\frac{5}{9}=\frac{35}{63}$$$

Add the fractions: $$$\frac{153}{63}+\frac{35}{63}=\frac{188}{63}$$$ (we just add the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $$$188$$$ as $$$2 \cdot 63+62$$$: $$$\frac{188}{63}=\frac{2 \cdot 63+62}{63}=2\frac{62}{63}$$$

So, $$$\frac{188}{63}=2\frac{62}{63}$$$

## Fractions subtraction

Multiply the numerator and the denominator of the first fraction by $$$9$$$: $$$\frac{17}{7}=\frac{153}{63}$$$

Multiple the numerator and the denominator of the second fraction by $$$7$$$: $$$\frac{5}{9}=\frac{35}{63}$$$

Subtract fractions: $$$\frac{153}{63}-\frac{35}{63}=\frac{118}{63}$$$ (we just subtract the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $$$118$$$ as $$$1 \cdot 63+55$$$: $$$\frac{118}{63}=\frac{1 \cdot 63+55}{63}=1\frac{55}{63}$$$

So, $$$\frac{118}{63}=1\frac{55}{63}$$$

## Fractions multiplication

Multiple the numerators and denominators: $$$\frac{17}{7} \cdot \frac{5}{9}=\frac{85}{63}$$$

Convert into a mixed number.

Rewrite $$$85$$$ as $$$1 \cdot 63+22$$$: $$$\frac{85}{63}=\frac{1 \cdot 63+22}{63}=1\frac{22}{63}$$$

So, $$$\frac{85}{63}=1\frac{22}{63}$$$

## Fractions division

Multiple the first fraction by inverted second fraction: $$$\frac{17}{7} \div \frac{5}{9}=\frac{17}{7} \cdot \frac{9}{5}=\frac{153}{35}$$$

Convert into a mixed number.

Rewrite $$$153$$$ as $$$4 \cdot 35+13$$$: $$$\frac{153}{35}=\frac{4 \cdot 35+13}{35}=4\frac{13}{35}$$$

So, $$$\frac{153}{35}=4\frac{13}{35}$$$

## Decimal representation

The decimal representation of $$$\frac{17}{7}$$$ is $$$2.42857142857143$$$

The decimal representation of $$$\frac{5}{9}$$$ is $$$0.555555555555556$$$

**Answer:**

$$$2\frac{3}{7}+ \left( \frac{5}{9} \right)=\frac{188}{63}=2\frac{62}{63}$$$

$$$2\frac{3}{7}- \left( \frac{5}{9} \right)=\frac{118}{63}=1\frac{55}{63}$$$

$$$2\frac{3}{7} \cdot \left( \frac{5}{9} \right)=\frac{85}{63}=1\frac{22}{63}$$$

$$$2\frac{3}{7} \div \left( \frac{5}{9} \right)=\frac{153}{35}=4\frac{13}{35}$$$

The decimal representation of $$$2\frac{3}{7}$$$ is $$$2.42857142857143$$$

The decimal representation of $$$\frac{5}{9}$$$ is $$$0.555555555555556$$$